객관식
How many electrons in an atom can have the quantum numbers n = 3, l = 2, m_l = 0?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
객관식
Which of the following sets of quantum numbers is allowed for an electron in an atom?
A
n = 1, l = 0, m_l = 1, m_s = +1/2
B
n = 2, l = 2, m_l = 0, m_s = -1/2
C
n = 3, l = 2, m_l = -2, m_s = +1/2
D
n = 4, l = 3, m_l = 4, m_s = -1/2
검증된 단계별 안내1
Recall the allowed ranges for each quantum number: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)).
The azimuthal quantum number \(l\) can take integer values from \(0\) up to \(n-1\) for a given \(n\) (i.e., \(l = 0, 1, 2, \ldots, n-1\)).
The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\) (i.e., \(m_l = -l, -(l-1), \ldots, 0, \ldots, (l-1), l\)).
The spin quantum number \(m_s\) can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
Check each set of quantum numbers against these rules to determine if they are allowed. For example, verify if \(m_l\) lies within \(-l\) to \(+l\) and if \(l\) is less than \(n\).
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